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MINIMAL HYPERSURFACES ASYMPTOTIC TO SIMONS CONES

Part of: Classical differential geometry

Published online by Cambridge University Press:  01 April 2015

Laurent Mazet
Laurent Mazet*
Affiliation:
Université Paris-Est, LAMA (UMR 8050), UPEC, UPEM, CNRS, 61, avenue du Général de Gaulle, F-94010 Créteil cedex, France (laurent.mazet@math.cnrs.fr)
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Abstract

In this paper, we prove that, up to similarity, there are only two minimal hypersurfaces in $\mathbb{R}^{n+2}$ that are asymptotic to a Simons cone, i.e., the minimal cone over the minimal hypersurface $\sqrt{\frac{p}{n}}\mathbb{S}^{p}\times \sqrt{\frac{n-p}{n}}\mathbb{S}^{n-p}$ of $\mathbb{S}^{n+1}$.

Keywords

minimal hypersurfacesSimons cone

MSC classification

Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 1 , February 2017 , pp. 39 - 58
Copyright
© Cambridge University Press 2015 

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